Do I need to set Speaker Configuration and Downmix?

See the manual (Setup Menu Options / Audio Processing Setup / Speaker Configuration).
The Speaker Configuration and Downmix settings are used only for multi-channel analog output, that is: the 5.1 or 7.1 analog cables.
You do not need to do anything with these settings if you are using any of:

a direct connection to the TV with HDMI or with stereo L/R cables

an HDMI connection to a receiver

a coaxial or optical connection to a receiver

a two-cable stereo connection to a receiver

What is DSD and how can I use this player's DSD features?

See the manual (Setup Menu Options / Audio Format Setup / SACD Output).
DSD over HDMI is a direct bitstream of an SACD Direct-Stream Digital format to your receiver. In order to use this feature you must have a receiver or processor that can decode DSD.
When the player is set to output DSD for SACD, the analog outputs will also output a direct DSD-to-analog conversion.
In both the above scenarios, you avoid a DSD-to-PCM conversion in the player. Setting the player for PCM output for SACD will output PCM over HDMI and also cause a DSD-to-PCM-to-analog conversion over analog outputs, which some people feel degrades the audio quality.

Does PCM have any advantages over DSD for SACD?

Setting SACD to PCM will allow the BDP-83's audio DSP to provide processing such as bass management, channel delays, channel trim, or Pro Logic II. It can't do those things when SACD is set to DSD. Volume control is also bypassed at the moment, but that may change in the future.
Despite the conversion concerns mentioned previously, PCM output for SACD will still produce a very high quality audio stream.

When converting DSD to PCM over HDMI, what is the highest resolution supported?

When the BDP-83 converts DSD to PCM internally, the resulting PCM data is 24bit/88.2kHz. This is the nominal processing rate produced by the conversion process, with no upsampling applied.

How do I switch between an SACD stereo mix and an SACD multi-channel mix?

Most SACD discs contain both a stereo mix and a multi-channel mix of the recording on the SACD layer. To switch between the stereo mix and the multi-channel mix of an SACD disc, press the Audio button on the remote.
However, selection of the CD layer contained on a hybrid SACD disc is not supported through the Audio button at this time. In order to select the CD layer of a hybrid SACD disc, you have to eject the disc and change SACD Priority as shown in the manual (Setup Menu Options / Playback Setup / SACD Priority).

Note

In early firmware it was reported that repeated switching back and forth between the SACD stereo mix and the multi-channel mix with the Audio button could render the playback of a disc unstable. In the context of an occasional switch the feature works normally. If the playback of a disc becomes unstable, eject the disc and start over.

Should I perform audio decoding in the player or in the receiver?

Bugs aside, there is no reason to expect that decoding in the OPPO and decoding in the AVR will produce different results.
The new "lossless" audio packing formats for Blu-ray (Dolby TrueHD and DTS-HD MA) are "lossless" in the sense that what comes out of the decoder is bit-for-bit identical to what went into the encoder in the first place when the studio created that track.
The result of decoding is high-bandwidth, multi-channel LPCM -- the simplest form of digital audio. The LPCM the OPPO sends out over the HDMI cable after decoding is the same LPCM as the AVR would get internally if it were asked to do the decoding.
The certification process from Dolby Labs and from DTS is supposed to ensure this.
The bottom line is that if you detect a quality difference in your setup, then you have likely discovered a bug or a user setup error -- either in the OPPO or in your AVR.
Note also that even if you like bitstreaming to your AVR, you still need to get an AVR that handles HDMI LPCM input properly -- because otherwise you won't be able to listen to the raw (uncompressed) LPCM tracks found on quite a few Blu-ray discs.
Letting the OPPO do the decoding also makes it easier to take advantage of "secondary audio mixing" on Blu-ray discs.
All in all, you might as well just let the OPPO do all the decoding and just leave it that way. Pretty much the only thing you lose will be that the little TrueHD or DTS-HD MA light won't turn on in your AVR because once the track has been decoded to LPCM the AVR can't tell what format it was prior to that.

What are the proper subwoofer/LFE settings?

redirecting a portion of the bass from other channels to the LFE output, making it into a "subwoofer" output (LFE and steered bass already combined).

The Short Version:

Bass management occurs in the player for analog output only. With digital, bass management happens in the AVR or prepro. So, if you are using analog, set the speaker sizes in the player. If you are using digital, set them in the AVR.

The only exception to doing analog bass management in the player occurs with a few expensive receivers that can redigitize the analog inputs. In those cases, the user should set speakers to large and output levels to 0db, which allows the AVR to handle bass management.

The OPPO outputs analog LFE -10db when speakers are set to large and -15db when any speakers are set to small.

With analog, the user needs to apply the 10db or 15db boost in his receiver or at the sub itself. Unlike digital, where the AVR software applies the needed boost, most receivers do not do this by default with analog. It's up to the user to apply it himself.

If the receiver cannot do the needed boost, you can add up to 10db of gain for the subwoofer channel in the OPPO. But that's not the recommended approach because it runs the risk of clipping during extremely loud passages.

SACD does not include the 10dB level difference in its LFE channel. (Why? I don't know).
The OPPO does the usual trick of lowering the LFE component of SACD content by 10dB and treating it from there just like a movie track. Which means the user need make no special adjustment in the receiver regardless of which output he is using from the OPPO. If you have it set up correctly for movies, you are also OK for SACD.

Please note that it is not particularly useful to compare what the OPPO is doing to what other players do, as many other players screw this up in one way or another. Even players from the major "audiophile" manufacturers have been known to ship with LFE level bugs of one form or another.

What is Secondary Audio?

Secondary Audio is an optional yak-track that goes with the Blu-ray Picture-in-Picture (PIP) feature. It is mixed in with the main audio so both tracks are audible together. See the manual (Basic Operations / Picture-in-Picture and Secondary Audio).
Like BD-Live and excessively complicated menus, it is a marketing-driven Blu-ray feature that no one ever asked for.

Is audio quality reduced when using Secondary Audio?

Yes, for some audio formats. See the two charts in the manual (Setup Menu Options / Audio Format Setup / Audio Signal Reference Chart). They show the different results for various formats and outputs when Secondary Audio is off and on.

Die, Secondary Audio, Die!

If you are concerned about Secondary Audio reducing your audio quality, do all of the following:

Turn off Secondary Audio in the Setup menu.

Use the on-disc menu of the title you are playing to turn off any PIP and SAP options that may be present.

How can I tell when Secondary Audio processing is being used?

The On Screen Display has a special icon for this.
On the lower left of the screen, the normal audio icon is three overlapping circles. When Secondary Audio processing is enabled, the icon changes to a jagged waveform.

Why am I not getting any Secondary Audio with my Picture-in-Picture?

Make sure you have Setup -> Audio Format Setup -> Secondary Audio set to On.

Some discs are authored in such a way that you must turn features off and on through the disc's menus; not everything can be done with the remote.For example, I have noticed this with several of Universal Studio's discs with "U-Control". You can toggle Picture-in-Picture on and off with the remote's PIP button, but toggling Secondary Audio on and off with the SAP button does not work unless you first turn on U-Control in the menu.Further, the disc's instructions state that U-Control can be toggled with the RED button; this works, but I've found you still get no SAP audio unless you do it with the menus.I've also encountered discs (Serenity, for example) where PIP and SAP cannot be toggled from the remote; everything has to be done from the disc menu or U-Control widget.

Can I toggle Secondary Audio on and off without using the setup menu?

No, not at the moment. The SAP button on the remote toggles the Secondary Audio track on off, but you have to use the Setup menu to turn off Secondary Audio processing completely. As to why you would want to, see Is audio quality reduced when using Secondary Audio?OPPO Digital has been working on this feature, but there are obstacles:

During early experiments it was found that some receivers take too long to switch between audio formats, causing a practical usability issue for on-the-fly switching.

Most recently released discs with SAP use BD-Java to control SAP mixing and the player has no overriding authority. With BD-Java, all the player can do is to pass a command or message to the Java program on the disc.